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ooo wrote:
> "Robert Maas, see http://tinyurl.com/uh3t"; <rem642b@xxxxxxxxx> wrote in
> message news:REM-2006dec30-001@xxxxxxxxxxxx
> > > From: "ooo" <fara...@xxxxxxxxx>
> > > If real line is filled with points and each point is
> > > distinguished,then each point has difference from every other
> > > points.
> >
> > Yes, however the difference from a given point to various other
> > points can be arbitrarily small (close to zero).
> > Between a given point and any other point on one side of it, there
> > are lots and lots of other points.
> Then all reals cannot be listed (I don't now apropreate words,but I don't
> mean reals is numbered, but rather cannot complehend. )
> If there are nowhere to be listed all reals in anyform,where they exist ,on
> real line? But we cannot take up all of them as a form we can deal with from
> there.
> > But there is no single place that is between a given point and all
> > other points on one side of it.
> >
> > > Therfore real line has void.
> >
> > Nope. Anywhere between real points you think there's a void, in
> > fact there's at least one real point in there to refute your void.
> >
> > It gets more interesting if you talk about voids between sets of
> > real points instead of between two singleton real points. Given any
> > two sets, where all the points of one are strictly less than all
> > the points of the second set, there is at least one real point
> > "between" the two sets in the sense that it is either:
> > - The very greatest element of the set of lesser points.
> > - The very least element of the set of greater points.
> > - Strictly between the two sets.
> Abobe explanation is similler to a case that berween any two reals ,there
> exist at least one real ,even though not so much .
> Please cosider follouing question I intended to posr another place.
> These arguments ,including Cantor's diagonal, mention up to countable
> case,and assume that these argument hold for infinite numbers objects.
> These arguments sometimes lead to confusion.
Cantor's diagonal argument shows that the real numbers are not
countable; where we mean by the statement "A is countable" that there
is a one-to-one correspondence, that is, a bijection, between the set
of natural numbers and A.
> In the question of vase and ball, argument is
> cardinarity of all added balls and that of removed balles is equevalent,
> hence at noon number of ball is 0 on the vase regardless process before
> then.
> Is it not the same with that cardinality of all naturas is equevalent with
> that of even numbers, so that naturals minus even numbers = 0.
> Why can it be ?
I can't understand what you have tried to mean. There are as many
naturals as the even ones are.
You seem to be a bit inefficient in English; it is no crime; we all
non-Englishmen have some lapse in our knowledge of English; in fact, I
am not an Englishman, and I ->do<- write wrong English, but it is not,
as you have mentioned, what I intend. If you are not sure whether what
you write is lucid, use mathematical notations as much as possible.
The correspondence : n |--------> 2n is a bijection between the
naturals and the even naturals.
>
> Regards OT
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